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Alcohol-based fuels for automobiles lead to the production of formaldehyde \(\left(\mathrm{CH}_{2} \mathrm{O}\right)\) in exhaust gases. Formaldehyde undergoes photodissociation, which contributes to photochemical smog: $$ \mathrm{CH}_{2} \mathrm{O}+h \nu \longrightarrow \mathrm{CHO}+\mathrm{H} $$ The maximum wavelength of light that can cause this reaction is \(335 \mathrm{nm} .(\mathbf{a})\) In what part of the electromagnetic spectrum is light with this wavelength found? (b) What is the maximum strength of a bond, in \(\mathrm{kJ} / \mathrm{mol}\), that can be broken by absorption of a photon of 335 -nm light? (c) Compare your answer from part (b) to the appropriate value from Table 8.3 . What do you conclude about \(\mathrm{C}-\mathrm{H}\) bond energy in formaldehyde? (d) Write out the formaldehyde photodissociation reaction, showing Lewis-dot structures.

Step by step solution

01

(a) Identifying the region of the electromagnetic spectrum

To find the electromagnetic spectrum region, we need to know the wavelength. We are given the wavelength as 335 nm. We can find the region by using the general classification guide, such as: - Ultraviolet (UV): 100 nm to 400 nm - Visible: 400 nm to 700 nm - Infrared (IR): 700 nm to 1 mm Our given wavelength of 335 nm falls under the ultraviolet (UV) category.

02

(b) Calculating the maximum bond strength

To find the maximum bond strength that can be broken by the absorption of 335 nm light, we need to use the formula: \(E = \cfrac{hc}{\lambda}\) where E is the energy per photon, h is the Planck's constant (6.626 x 10^{-34} Js), c is the speed of light (3 x 10^8 m/s), and \(\lambda\) is the wavelength. First, we need to convert \(\lambda\) to meters: \(335\ nm = 335 \times 10^{-9}\ m\) Now we can find the energy per photon: \(E = \cfrac{6.626 \times 10^{-34}\ Js \times 3.00 \times 10^8\ m/s}{335 \times 10^{-9}\ m} = 5.929 \times 10^{-19}\ J/photon\) To find the energy per mole of photons, we multiply by Avogadro's number \(N_A (6.022 \times 10^{23} mol^{-1})\): \(E_{mol} = 5.929 \times 10^{-19}\ J/photon \times 6.022 \times 10^{23}\ mol^{-1} = 356.911 \times 10^3\ J/mol = 356.9\ kJ/mol\) So, the maximum bond strength that can be broken is 356.9 kJ/mol.

03

(c) Comparing the C-H bond energy

Referring to Table 8.3, the C-H bond energy in formaldehyde is 339 kJ/mol. Comparing this with the bond energy found in part (b), we can see that the bond energy of formaldehyde is less than the energy per mole of photons (339 kJ/mol < 356.9 kJ/mol). Therefore, the C-H bond in formaldehyde can be broken by 335 nm light.

04

(d) Formaldehyde photodissociation reaction with Lewis-dot structures

Formaldehyde (\(\mathrm{CH_2O}\)) has a central carbon (C) atom with a double bond to an oxygen (O) atom and two single bonds to two hydrogen (H) atoms: O = C - H | H The photodissociation reaction, showing Lewis-dot structures, occurs as follows: O H 鈺� C - H + h谓 鉄� O + H | H

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Electromagnetic Spectrum

Light is all around us, and it comes in different forms, each possessing unique characteristics. The electromagnetic spectrum is the range of all types of electromagnetic radiation. Different forms of electromagnetic radiation are classified based on wavelength. This range includes everything from radio waves to gamma rays. For this exercise, the focus is on ultraviolet (UV) light. When considering the photodissociation of formaldehyde, it's essential to note that the light involved has a wavelength of 335 nm.

This wavelength is part of the UV region of the electromagnetic spectrum. Specifically:

• Ultraviolet (UV) light: 100 nm to 400 nm
• Visible light: 400 nm to 700 nm
• Infrared (IR) light: 700 nm to 1 mm

Therefore, the light responsible for breaking the formaldehyde bonds falls into the UV category, emphasizing the need for careful consideration of how UV exposure affects chemical reactions.

Bond Energy Calculation

Understanding how much energy is needed to break a chemical bond is crucial in chemistry. The energy required to break a bond through light absorption is directly related to the wavelength of the light used. This exercise uses the equation:
\[ E = \frac{hc}{\lambda} \]where:

• \(E\) is the energy per photon,
• \(h\) is Planck's constant \(6.626 \times 10^{-34}\) Js,
• \(c\) is the speed of light \(3 \times 10^{8}\) m/s,
• \(\lambda\) is the wavelength \(335\, nm\).

By substituting these values into the formula, the energy per photon can be calculated, leading to the determination of energy per mole by multiplying with Avogadro's number \(6.022 \times 10^{23}\, mol^{-1}\). This results in a maximum bond energy of \(356.9\, kJ/mol\). Recognizing this value allows for determining whether light at this wavelength can break certain chemical bonds.

Lewis Dot Structures

Lewis dot structures visually represent how atoms are bonded within a molecule, showing shared or transferred electrons as dots. In formaldehyde, \(\mathrm{CH_2O}\), the carbon atom forms a double bond with an oxygen atom and single bonds with two hydrogen atoms. This molecule is often depicted as:
O = C - H | H

In these structures, the 'dots' represent valence electrons that participate in forming bonds. Understanding these representations helps envision the types of bonds in a molecule and predict how they might react or break during dissociation processes, like when UV light is absorbed.

Photochemical Smog

Photochemical smog is a type of air pollution resulting from the reaction between sunlight and pollutants such as hydrocarbons and nitrogen oxides. Formaldehyde plays a role in this process due to its photodissociation, which releases reactive radicals into the atmosphere, contributing to smog formation. In photochemical reactions, components like \(\mathrm{CHO}\) and \(\mathrm{H}\) play significant roles in further reactions leading to smog.

This understanding highlights the importance of regulating emissions from vehicles and industrial processes, as their by-products can react under sunlight to worsen air quality. Recognizing formaldehyde's capacity to form reactive radicals under UV light underscores why its control in exhaust gases is vital for minimizing smog.